On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms

We study the geometrically nonlinear behavior of uniformly compressed tensegrity prisms, through fully elastic and rigid--elastic models. The presented models predict a variety of mechanical behaviors in the regime of large displacements, including an extreme stiffening-type response, already known in the literature, and a newly discovered, extreme softening behavior. The latter may lead to a snap buckling event producing an axial collapse of the structure. The switching from one mechanical regime to another depends on the aspect ratio of the structure, the magnitude of the applied prestress, and the material properties of the constituent elements. We discuss potential acoustic applications of such behaviors, which are related to the design and manufacture of tensegrity lattices and innovative phononic crystals

On the compact wave dynamics of tensegrity beams in multiple dimensions

This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams reveal - for the first time - the presence of compact compression waves in two- and three-dimensional tensegrity lattices with slender aspect ratio. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices

Parametric Design of Minimal Mass Tensegrity Bridges Under Yielding and Buckling Constraints

This paper investigates the use of the most fundamental elements; cables for tension and bars for compression, in the search for the most efficient bridges. Stable arrangements of these elements are called tensegrity structures. We show herein the minimal mass arrangement of these basic elements to satisfy both yielding and buckling constraints. We show that the minimal mass solution for a simply-supported bridge subject to buckling constraints matches Michell's 1904 paper which treats the case of only yield constraints, even though our boundary conditions differ. The necessary and sufficient condition is given for the minimal mass bridge to lie totally above (or below) deck. Furthermore this condition depends only on material properties. If one ignores joint mass, and considers only bridges above deck level, the optimal complexity (number of elements in the bridge) tends toward infinity (producing a material continuum). If joint mass is considered then the optimal complexity is finite. The optimal (minimal mass) bridge below deck has the smallest possible complexity (and therefore cheaper to build), and under reasonable material choices, yields the smallest mass bridge.Comment: 56 pages, 25 figures, 13 tables. Internal Report 2014-1: University of California, San Diego, 201

Experimental investigation of the softening-stiffening response of tensegrity prisms under compressive loading

The present paper is concerned with the formulation of new assembly methods of bi-material tensegrity prisms, and the experimental characterization of the compressive response of such structures. The presented assembly techniques are easy to implement, including a string-first approach in the case of ordinary tensegrity prisms, and a base-first approach in the case of systems equipped with rigid bases. The experimental section shows that the compressive response of tensegrity prisms switches from stiffening to softening under large displacements, in dependence on the current values of suitable geometric and prestress variables. Future research lines regarding the mechanical modeling of tensegrity prisms and their use as building blocks of nonlinear periodic lattices and acoustic metamaterials are discussed

A variational constitutive model for soft biological tissues

In this paper, a fully variational constitutive model of soft biological tissues is formulated in the finite strain regime. The model includes Ogden-type hyperelasticity, finite viscosity, deviatoric and volumetric plasticity, rate and microinertia effects. Variational updates are obtained via time discretization and pre-minimization of a suitable objective function with respect to internal variables. Genetic algorithms are used for model parameter identification due to their suitability for non-convex, high dimensional optimization problems. The material behavior predicted by the model is compared to available tests on swine and human brain tissue. The ability of the model to predict a wide range of experimentally observed behavior, including hysteresis, cyclic softening, rate effects, and plastic deformation is demonstrated

A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions

The equilibrium problem of unreinforced masonry vaults is analyzed via a constrained thrust network approach. The masonry structure is modeled as no-tension membrane (thrust surface) carrying a discrete network of compressive singular stresses, through a non-conforming variational approximation of the continuous problem. The geometry of the thrust surface and the associated stress field are determined by means of a predictor–corrector procedure based on polyhedral approximations of the thrust surface and membrane stress potential. The proposed procedure estimates the regions exposed to fracture damage according to the no-tension model of the masonry. Some numerical results on the thrust network and crack pattern of representative vault schemes are given

A multiscale approach to the elastic moduli of biomembrane networks

We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172–180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473–2480, 2005; Hale et al. in SoftMatter 5:3603–3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528–540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBCmodel.We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature

On a Moderate Rotation Theory of Thin-Walled Composite Beams

A small strain and moderate rotation theory of laminated composite thin-walled beams is formulated by generalizing the classical Vlasov theory of sectorial areas. The proposed beam model accounts for axial, bending, torsion and warping deformations and allows one to predict critical loads and initial post-buckling behaviour. A finite element approximation of the theory is also carried out and several numerical applications are developed with reference to lateral buckling of composite thin-walled members. The sensitivity of critical load to secondorder effects in the pre-buckling range is pointed out